Calculating Dart Scores

In a game of darts a player throws darts at a board
consisting of 20 different sections labelled $1$ to $20$. When the dart hits section
$i$ the player scores
$i$ points. Each section
also contains a double area and a triple
area. When the dart hits the double area of section
$i$ the player scores
$2 i$ points, and when the
dart hits the triple area the player scores
$3 i$ points, instead of
$i$ points. When throwing
three darts, the player can therefore score a total of at most
$180$ points by throwing
all three darts in the triple area of section $20$.

Given a target score, output at most three throw scores such
that their sum is equal to the given target score. Note that
the centre of the dartboard, which is usually called bullseye,
is not taken into account is this problem.

Input

The input consists of a single integer $n$ ($1\leq n \leq 180$), the target
score.

Output

If the target score can be achieved, output at most three
lines, each of the form “single
$d$”, “double $d$”, or “triple $d$”, where $d$ is an integer between $1$ and $20$ (inclusive), such that the sum of
these scores is equal to $n$. Otherwise, output “impossible”. If there are multiple valid
answers you may output any of them.